Segal-Bargmann transform for generalized partial-slice monogenic functions

Abstract: The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to develop the Segal-Bargmann transform and give a Schr\"{o}dinger representation in the setting of generalized partial-slice monogenic functions. To this end, the generalized partial-slice Cauchy-Kovalevskaya extension plays a crucial role.